Average Error: 0.0 → 0
Time: 5.7s
Precision: 64
\[x \cdot \left(y + 1\right)\]
↓
\[\mathsf{fma}\left(y, x, x \cdot 1\right)\]
x \cdot \left(y + 1\right)
↓
\mathsf{fma}\left(y, x, x \cdot 1\right)
double f(double x, double y) {
        double r584155 = x;
        double r584156 = y;
        double r584157 = 1.0;
        double r584158 = r584156 + r584157;
        double r584159 = r584155 * r584158;
        return r584159;
}
↓
double f(double x, double y) {
        double r584160 = y;
        double r584161 = x;
        double r584162 = 1.0;
        double r584163 = r584161 * r584162;
        double r584164 = fma(r584160, r584161, r584163);
        return r584164;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0.0
Herbie0
\[x + x \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(y + 1\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{x \cdot y + x \cdot 1}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{y \cdot x} + x \cdot 1\]
  5. Using strategy rm

  6. Applied fma-def0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, x \cdot 1\right)}\]

  7. Final simplification0

    \[\leadsto \mathsf{fma}\left(y, x, x \cdot 1\right)\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, B"

  :herbie-target
  (+ x (* x y))

  (* x (+ y 1.0)))